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ec_curvedata • Show schema
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{'Ciso': '431970bz', 'Clabel': '431970bz4', 'Cnumber': 4, 'abc_quality': 1.0111434690046417, 'absD': 132654615198381430197120, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 22440, 'ainvs': [1, 0, 1, -102111419, -396776314618], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 11, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 431970, 'degree': 91750400, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.3506558855714931926636728603', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 51, 'isogeny_degrees': [1, 2, 4], 'jinv': [66464620505913166201729, 74880071980801920], 'lmfdb_iso': '431970.bz', 'lmfdb_label': '431970.bz1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -843896, 298027200], 'min_quad_twist_disc': -11, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '88.12.0.?', '120.12.0.?', '136.12.0.?', '660.12.0.?', '1320.24.0.?', '1496.24.0.?', '2040.24.0.?', '22440.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 6, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.5830321203602953832342246948', 'prec': 100}, 'semistable': False, 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.1517082491723079206327010713', 'prec': 100}, 'szpiro_ratio': 5.158581504486995, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 0, 1, 6, 1, -1, 1, -1, -1, 4, -1], 'aplist': [-1, 1, -1, -1, 0, 6, -1, 4, -4, -2, -4, -6, 2, 0, 8, -10, -8, 6, 0, 0, -6, -12, 12, -6, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 431970, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '431970.bz', 'trace_hash': 1015188283139336836}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.0012292982865389211863004940575', 'prec': 110}, 'conductor': 431970, 'gens': [[-5910, 19861, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.5830321203602953832342246948', 'prec': 100}], 'lmfdb_label': '431970.bz1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.047496363016381653545974519383', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.8072397715195308459663073568130662900', 'prec': 130}, 'tamagawa_product': 40, 'torsion_generators': [[-23929, 23925, 2]], 'xcoord_integral_points': [-5910, 66648]}
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lmfdb_label 431970.bz1 does not appear in ec_iwasawa
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lmfdb_label 431970.bz1 does not appear in ec_torsion_growth
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ec_localdata • Show schema
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id: 10667538
{'conductor': 431970, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '431970.bz1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 10667539
{'conductor': 431970, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '431970.bz1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 5}
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id: 10667540
{'conductor': 431970, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '431970.bz1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 10667541
{'conductor': 431970, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '431970.bz1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 10667542
{'conductor': 431970, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '431970.bz1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 10667543
{'conductor': 431970, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '431970.bz1', 'prime': 17, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 4329812
{'adelic_gens': [[14521, 10208, 7084, 18393], [7, 6, 22434, 22435], [10968, 1793, 4873, 13080], [1, 0, 8, 1], [19724, 4081, 19063, 20406], [8416, 7403, 19129, 21198], [22433, 8, 22432, 9], [4079, 0, 0, 22439], [3268, 4081, 8591, 20406], [1, 8, 0, 1], [1, 4, 4, 17]], 'adelic_image': '22440.48.0.?', 'conductor': 431970, 'lmfdb_label': '431970.bz1', 'prime': 0}
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id: 1452323
{'conductor': 431970, 'elladic_image': '4.6.0.1', 'lmfdb_label': '431970.bz1', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 431970.bz does not appear in ec_padic